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Simplifying 6x2 + 32x + 30 = x2 + x Reorder the terms: 30 + 32x + 6x2 = x2 + x Reorder the terms: 30 + 32x + 6x2 = x + x2 Solving 30 + 32x + 6x2 = x + x2 Solving for variable 'x'. Reorder the terms: 30 + 32x + -1x + 6x2 + -1x2 = x + x2 + -1x + -1x2 Combine like terms: 32x + -1x = 31x 30 + 31x + 6x2 + -1x2 = x + x2 + -1x + -1x2 Combine like terms: 6x2 + -1x2 = 5x2 30 + 31x + 5x2 = x + x2 + -1x + -1x2 Reorder the terms: 30 + 31x + 5x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 30 + 31x + 5x2 = 0 + x2 + -1x2 30 + 31x + 5x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 30 + 31x + 5x2 = 0 Factor a trinomial. (5 + x)(6 + 5x) = 0Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(6 + 5x)' equal to zero and attempt to solve: Simplifying 6 + 5x = 0 Solving 6 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5x = 0 + -6 5x = 0 + -6 Combine like terms: 0 + -6 = -6 5x = -6 Divide each side by '5'. x = -1.2 Simplifying x = -1.2Solution
x = {-5, -1.2}
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